Solving Real-World Linear Programs: A Decade and More of Progress

By Robert E. Bixby. Operational Research, 2002

425 citations recorded by the source corpus.

Subfields: Computer Networks and Communications, Industrial and Manufacturing Engineering, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/a90c20f0909a11fc224566724540a550dc764dc4

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Citations in the corpus

Interior Point Methods for Nonlinear Optimization (2010, neutral): “com CPLEX [12], http://www.”
Tight and Compact MILP Formulation for the Thermal Unit Commitment Problem (2013, background): “Although the number of constraints is considered to be the best simple predictor of the LP models’ difficulty [16], [17], the number of nonzeros also has a significant impact on solution times [10].”
Ship Routing and Scheduling: Status and Perspectives (2004, methodology): “According to Bixby (2002), an LP model that might have taken a year to solve 10 years ago, can now be solved in less than 30 seconds.”
Selected Topics in Column Generation (2002, background): “For some linear programs Barrier methods (Bixby 2002) can prove most effective, although there is no possible warm start.”
Invitation to data reduction and problem kernelization (2007, background): “Bixby [5] describes a large linear program that can be solved in half an hour when data reduction is employed but is “far from even being feasible” for the non-reduced instance even after hours of computation.”
Optimal Transmission Switching (2008, neutral): “In addition, progress is being made on solution techniques [20].”
A mixed integer programming solution for market clearing and reliability analysis (2005, background): “Programming (LP) executions, they have benefited from recent advances in both computer hardware and software [ 6 ].”
Linear Programming Relaxations and Belief Propagation - An Empirical Study (2006, background): “Indeed as the original programmer of CPLEX notes “the solution of integer programs is the dominant application of linear programming in practice” (Bixby, 2001) and CPLEX contains a large number of optimizations that are based on exploiting the sparse structure of LPs that arise from LP relaxations (”
The interior-point revolution in optimization: History, recent developments, and lasting consequences (2004, background): “In LP today, interior methods are faster than simplex for some very large problems, the reverse is true for some problems, and the two approaches are more or less comparable on others; see [2].”
A Brief History of Linear and Mixed-Integer Programming Computation (2012, background): “For the CPLEX code, many of these developments are documented in [7] .”
MIPLIB 2010 - Mixed Integer Programming Library version 5 (2011, neutral): “It is recorded in various articles [22,72,77] and numerous talks.”